Fairfax Fare actually used to be called Fairfax Fries, and was located back down Sunset Boulevard where Toluca Legs Turkey Co. is today. Back then, Fairfax Fries was the place in the Studios to buy McDonalds french fries. Disney severed its ties with McDonalds back in the 2000s, and the restaurant changed its name and location.
The name Fairfax Fries (and Fairfax Fare) refers to Fairfax Avenue in Los Angeles, California. Why Fairfax Avenue? Well, the Sunset Ranch Market area of Sunset Boulevard is based on the Los Angeles Farmers Market that is located at Fairfax and Third Street and since both Fairfax Fries and Fairfax Fare are part of the area, the name pay homage to the street in Los Angeles that is part of the farmers market.